Hamilton-Jacobi equation, heteroclinic chains and Arnol'd diffusion in three time scale systems

Interacting systems consisting of two rotators and a point mass near a hype rbolic fixed point are considered, in a case in which the uncoupled systems have three very different characteristic time scales. The abundance of qua si periodic motions in phase space is studied via the Hamilton-Jacobi equat ion. The main result, a high density theorem of invariant tori, is derived by the classical canonical transformation method extending previous results . As an application the existence of long heteroclinic chains (and of Arnol 'd diffusion) is proved for systems interacting through a trigonometric pol ynomial in the angle variables. AMS classification scheme numbers: 37J40, 3 7J45, 58F27, 34C37.